As approximation technique inevitably introduces imprecision, giving tighter approximation is crucial to obtaining more precise verification results. Previous works mainly provide tighter certified robustness bounds by gradually narrowing the input-output zone between the bound and linear constraint of non-linear function. Henriksen et al. [1]} propose VeriNet and gives linear constraints for Sigmoid/Arctan/Tanh function by producing the minimal input-output zone. By Definition REF , VeriNet is the Neuron-wise Tightest technique for robustness verification of CNNs with Sigmoid/Arctan/Tanh function and stands for the highest precision in the sequel of narrowing the zone. As shown in FigureREF , VeriNet produces smaller over-approximation zone than DeepCert, which is the most recent work.
